A course in analysis
- Niels Jacob, Kristian P. Evans (Swansea University, UK).
- New Jersey : World Scientific, -
- Physical description
- volumes : illustrations ; 26 cm
At the library
Science Library (Li and Ma)
Library has: v.1-
|QA300 .J27 2016 V.1||Unknown|
|QA300 .J27 2016 V.2||Unknown|
|QA300 .J27 2016 V.3||Unknown|
|QA300 .J27 2016 V.4||Unknown|
- Includes bibliographical references and index.
- Introductory Calculus: Numbers - Revision-- The Absolute Value, Inequalities and Intervals-- Mathematical Induction-- Functions and Mappings-- Functions and Mappings Continued-- Derivatives-- Derivatives Continued-- The Derivative as a Tool to Investigate Functions-- The Exponential and Logarithmic Functions-- Trigonometric Functions and Their Inverses-- Investigating Functions-- Integrating Functions-- Rules for Integration-- Analysis in One Dimension: Problems with the Real Line-- Sequences and their Limits-- A First Encounter with Series-- The Completeness of the Real Numbers-- Convergence Criteria for Series, b-adic Fractions-- Point Sets in Continuous Functions-- Differentiation-- Applications of the Derivative-- Convex Functions and some Norms on n-- Uniform Convergence and Interchanging Limits-- The Riemann Integral-- The Fundamental Theorem of Calculus-- A First Encounter with Differential Equations-- Improper Integrals and the GAMMA-Function-- Power Series and Taylor Series-- Infinite Products and the Gauss Integral-- More on the GAMMA-Function-- Selected Topics on Functions of a Real Variable--.
- (source: Nielsen Book Data)9789814689090 20160619
- Publisher's Summary
- Volume 1 covers the content of two typical modules in undergraduate course for mathematics: Part 1: Introductory calculus Part 2: Analysis of functions of one variableThese two parts are divided into 32 chapters. Part 1 begins with an overview of a set of real numbers: rational and irrational. This is accompanied by a discussion of arithmetic rules, inequalities, absolute values. Doing this, the authors, in a clever way, introduce elements of a set theory using Cantor's approach. This is followed by the definition of a function and discussion of operations on functions. From this they move to differential and integral calculus and their applications.Part 2 contains rigorous proofs of theorems from Part 1. In particular, they introduce the order structure on a real line using axioms of an ordered field. It is worth mentioning that Part 2 contains elements of topology obviously on real line and a good insight on convex functions. The convex functions relate Analysis to linear spaces equipped with norm. Finally, to close Part 2 the authors supply a number of Appendices, among them Appendices on logic, set theory and Peano axioms.Remarkably, Volume 1 contains 360 problems with complete solutions.
(source: Nielsen Book Data)9789814689090 20160619
- Beginning date
- 9789814689083 (v. 1 : hardcover : alk. paper)
- 9814689084 (v. 1 : hardcover : alk. paper)
- 9789814689090 (v. 1 : pbk : alk. paper)
- 9814689092 (v. 1 : pbk : alk. paper)
- 9789813140950 (v. 2 : hardcover : alk. paper)
- 9789813221598 (v. 3 : hardcover : alk. paper)
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